Right orthogonal class of pure projective modules over pure hereditary rings

Let $\mathcal{W}$ be the class of all pure projective modules. In this article, $\mathcal{W}$-injective modules is defined via the vanishing of cohomology of pure projective modules. First we show that every module has a $\mathcal{W}$-injective coresolution over an arbitrary ring and the class of all $\mathcal{W}$-injective modules is coresolving over a pure-hereditary ring. Further, we analyze the dimension of $\mathcal{W}$-injective coresolution over a pure-hereditary ring. It is shown that \Fcor_{\mathcal{W}^{\bot}}(R) = \sup\{\pd(G) \colon G is a pure projective $R$-module\} = \sup\{\cores_{\mathcal{W}^{\bot}}(M) \colon M is an $R$-module$\}.$ Finally, we give some equivalent conditions of $\mathcal{W}$-injective envelope with the unique mapping property. The dimension has desirable properties when the ring is semisimple artinian.Comment: 17 pages, 9 figure

Amalgamated rings with m-nil clean properties

A ring is called m-nil clean if every element is a sum of a nilpotentand an m-potent element. We study some properties of m-nil cleanring and we also investigate the transfer of m-nil clean property to theamalgamated algebra of R with S along J with respect to

Bi-amalgamated algebra with (n; p)-weakly clean like properties

Let f : A −→ B and g : A −→ C be two ring homomorphisms and let K and K′ be two ideals of B and C, respectively such that f −1(K) = g−1(K′). In this paper, we give a characterization for the bi-amalgamation of A with (B, C) along (K, K′) with respect to (f, g) (denoted by A ▷◁f,g (K, K′)) to be a (n, p)-weakly clean ring

Amalgamated rings with m-nil clean properties

In this paper, we study the transfer of the notion of $m$-nil clean (i.e., a ring in which  every element is a sum of a nilpotent and  an $m$-potent elements) to the amalgamarted rings. We also find many sufficient and necessary conditions for the   $m$-nil clean property  to the amalgamated rings

The Eye: A Light Weight Mobile Application for Visually Challenged People Using Improved YOLOv5l Algorithm

The eye is an essential sensory organ that allows us to perceive our surroundings at a glance. Losing this sense can result in numerous challenges in daily life. However, society is designed for the majority, which can create even more difficulties for visually impaired individuals. Therefore, empowering them and promoting self-reliance are crucial. To address this need, we propose a new Android application called “The Eye” that utilizes Machine Learning (ML)-based object detection techniques to recognize objects in real-time using a smartphone camera or a camera attached to a stick. The article proposed an improved YOLOv5l algorithm to improve object detection in visual applications. YOLOv5l has a larger model size and captures more complex features and details, leading to enhanced object detection accuracy compared to smaller variants like YOLOv5s and YOLOv5m. The primary enhancement in the improved YOLOv5l algorithm is integrating L1 and L2 regularization techniques. These techniques prevent overfitting and improve generalization by adding a regularization term to the loss function during training. Our approach combines image processing and text-to-speech conversion modules to produce reliable results. The Android text-to-speech module is then used to convert the object recognition results into an audio output. According to the experimental results, the improved YOLOv5l has higher detection accuracy than the original YOLOv5 and can detect small, multiple, and overlapped targets with higher accuracy. This study contributes to the advancement of technology to help visually impaired individuals become more self-sufficient and confident. Doi: 10.28991/ESJ-2023-07-05-011 Full Text: PD

Some results on GCG_C-flat dimension of modules

summary:In this paper, we study some properties of $G_C$-flat $R$-modules, where $C$ is a semidualizing module over a commutative ring $R$ and we investigate the relation between the $G_C$-yoke with the $C$-yoke of a module as well as the relation between the $G_C$-flat resolution and the flat resolution of a module over $GF$-closed rings. We also obtain a criterion for computing the $G_C$-flat dimension of modules

Weak nn-injective and weak nn-fat modules

summary:We introduce and study the concepts of weak $n$-injective and weak $n$-flat modules in terms of super finitely presented modules whose projective dimension is at most $n$, which generalize the $n$-FP-injective and $n$-flat modules. We show that the class of all weak $n$-injective $R$-modules is injectively resolving, whereas that of weak $n$-flat right \hbox {$R$-modules} is projectively resolving and the class of weak $n$-injective (or weak $n$-flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.\looseness +